A308232 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the concatenation kd, d being the digit that was read and k the number of d's present so far in the sequence.

1, 11, 21, 31, 12, 41, 13, 51, 61, 22, 14, 71, 81, 23, 15, 91, 16, 101, 32, 42, 111, 24, 17, 121, 18, 131, 52, 33, 141, 25, 19, 151, 161, 26, 171, 10, 181, 43, 62, 34, 72, 191, 201, 211, 82, 44, 221, 27, 231, 92, 241, 251, 28, 261, 53, 271, 35, 102, 63, 73, 281, 54, 291, 112, 45, 301, 29, 311, 55, 321, 331, 36, 341, 122, 46, 351

Offset: 1

Author

Eric Angelini and Carole Dubois, May 16 2019

Keywords

• base
• nonn

Comments

All integers > 0 will appear exactly once, except 2, 3, 4, 5, 6, 7, 8 and 9 which will never appear.

Examples

			The sequence starts with a(1) = 1.
We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then [kd] = 11 and this 11 becomes a(2);
We read now the first digit of a(2) = 11, which is 1; as this 1 is the 2nd occurrence of 1 so far in the sequence, we have k = 2 and [kd] = 21; this 21 becomes a(3);
We read now the second digit of a(2) = 11, which is 1; as this 1 is the 3rd occurrence of 1 so far in the sequence, we have k = 3 and [kd] = 31; this 31 becomes a(4);
We read now the first digit of a(3) = 21, which is 2; as this 2 is the 1st occurrence of 2 so far in the sequence, we have k = 1 and [kd] = 12; this 12 becomes a(5);
We read now the second digit of a(3) = 21, which is 1; as this 1 is the 4th occurrence of 1 so far in the sequence, we have k = 4 and [kd] = 41; this 41 becomes a(6); etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5001
• Carole Dubois, Digit count for three sequences (see Xrefs)
• Carole Dubois, Digit-count for this sequence and two others visible in the Xref section

Crossrefs

Cf. A325721 and A325722 where the same idea is developed (addition and multiplication instead of concatenation).